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Magnetic properties of a Ho2Fe14Si3 single crystal
Journal of Alloys and Compounds 694 (2017) 761e766
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Magnetic properties of a Ho2Fe14Si3 single crystal A.V. Andreev a, *, D.I. Gorbunov b, Y. Skourski b, M.D. Kuz'min c, E.A. Tereshina a, M.S. Henriques a a
Institute of Physics, Academy of Sciences, Na Slovance 2, 182 21 Prague, Czechia Dresden High Magnetic Field Laboratory (HLD-EMFL), Helmholtz-Zentrum, Dresden-Rossendorf, D-01314 Dresden, Germany c Aix-Marseille Universit e, IM2NP, UMR CNRS 7334, 13397 Marseille, France b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 June 2016 Received in revised form 6 October 2016 Accepted 8 October 2016 Available online 10 October 2016
Magnetization of a Ho2Fe14Si3 single crystal was measured in a steady magnetic field of up to 9 T and in pulsed fields of up to 60 T applied along the principal axes. Ho2Fe14Si3 is a ferrimagnet below TC ¼ 480 K, has a spontaneous magnetic moment of about 8 mB/f.u. (at T ¼ 4.2 K) and exhibits a large easy-plane magnetic anisotropy. There is also a certain anisotropy within the basal plane, the b axis [120] being the easy-magnetization direction. In fields applied along the a and b axes field-induced first-order phase transitions are observed at 29 T and at 22 T, respectively. Along the easy axis b we observe also an Sshaped anomaly at about 47 T, which does not correspond to a phase transition. A simple model predicts that the two observed first-order transitions are the only ones taking place in Ho2Fe14Si3; the magnetization should subsequently grow continuously and arrive at saturation at ~100 T. This is in stark contrast to the behavior of the parent compound Ho2Fe17, where as many as three sequential first-order transitions are expected for Hjjb. The reason for the disparity is that the basal-plane anisotropy constant KHo is at least one order of magnitude smaller in Ho2Fe14Si3 than it is in Ho2Fe17. © 2016 Elsevier B.V. All rights reserved.
Keywords: Rare-earth intermetallics R2T17 High magnetic fields Field-induced transitions Magnetic anisotropy
1. Introduction The magnetism of rare earth (R) intermetallic compounds with iron and/or cobalt is of interest from two points of view. Firstly, because of the high application potential of these materials, e.g., as permanent magnets (primarily R2Fe14B-based). Secondly, from a purely academic prospective, these are systems containing two entirely distinct kinds of electrons: (i) the 4f electrons, localized within the R atoms, and (ii) the itinerant 3d electrons of Fe or Co. The competition of intra- and inter-sublattice exchange interactions with each other and with the crystal field often brings about spontaneous and/or field-induced magnetic phase transitions. Research into these phenomena is conducive to deeper understanding of the fundamental aspects of magnetism but it is also of great practical importance. Suffice it to recall that the anisotropy (and coercivity) of permanent magnets at and above room temperature is proportional to the leading crystal field parameter A20 times the square of the inter-sublattice exchange field [1]. Ho2Fe17 crystallizes in the hexagonal crystal structure of the
* Corresponding author. E-mail address: [email protected] (A.V. Andreev). http://dx.doi.org/10.1016/j.jallcom.2016.10.069 0925-8388/© 2016 Elsevier B.V. All rights reserved.
Th2Ni17 type, characteristic of the heavy R. Magnetic measurements on single crystals showed that in the ground state the spontaneous magnetic moment, Ms ¼ 16.0e18.5 mB/f.u. (per formula unit), lies in the basal plane along the [210] direction (or the b axis in the orthorhombic coordinates) [2e6]. The compound is a collinear ferrimagnet below the Curie temperature, TC ¼ 325e335 K [2,5,7,8]. The total magnetic moment is parallel to that of the Fe sublattice. Taking Ms ¼ 18 mB/f.u. ([6]) and the magnetic moment of the Ho sublattice MHo ¼ 20 mB/f.u. (as 2 free-ion moments of Ho3þ), the Fe sublattice moment MFe is found to be 38 mB/f.u. In such compounds, field-induced phase transitions are expected, from the collinear ferrimagnetic structure, through intermediate canted structures, to the final collinear ferromagnetic configuration. This was observed in Ho2Co17 [9] and in several other ferrimagnetic R2Fe17 and R2Co17 compounds with the easy-plane type of anisotropy. The high-field magnetic transitions that take place in these compounds in a magnetic field applied within the basal-plane are the result of competition between the Zeeman energy (strength of the applied field) and the energy of the 3d-4f exchange interaction. In particular, step-wise anomalies were observed in the high-field magnetization curves of Ho2Fe17: at 45 T when the field was applied along the b axis, and at 55 T when it was along the a axis [6]. In the maximum available field (60 T) the magnetization reached 34 mB/
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f.u.; this is still far below the value characteristic of the collinear ferromagnetic state, 48 mB. Magnetization of the Si solid solutions in R2Fe17, R2Fe14Si3, was studied on polycrystalline samples [8]. A strong modification of both the intra- and inter-sublattice interactions was found in R2Fe14Si3 as compared with R2Fe17. The effect is rather complicated, because the Fe sublattice moment is weakened by the dilution with the non-magnetic Si, whereas the Fe-Fe exchange interaction is unexpectedly enhanced e so the Curie temperature rises from 330 K in Ho2Fe17 to 477 K in Ho2Fe14Si3 [8]. If it is true that the strength of the inter-sublattice exchange coupling is reduced by the dilution of the Fe sublattice, then in the silicides the transitions should take place in lower, more easily attainable fields. Previously we studied the high-field magnetization of Dy2Fe14Si3 [10] and found that the transition fields had decreased in comparison with those in the binary compound Dy2Fe17. Thus, the critical field along the a axis amounted to 33 T and 54 T, respectively, in Dy2Fe14Si3 and in Dy2Fe17. Along the b axis, the transition was observed at 39 T in Dy2Fe14Si3, whereas in Dy2Fe17 it did not take place up to 60 T. If a similar behavior is valid for the Ho compounds, we can expect to see more transitions in a field up to 60 T, get closer to the forced ferromagnetic state and check in this way our description of the high-field magnetization process in R2Fe17 developed in Refs. [6,10]. In the present work we measured the magnetization of Ho2Fe14Si3 in steady and pulsed magnetic fields applied along the principal crystallographic axes. 2. Experimental A single crystal of Ho2Fe14Si3, 25 mm long and 4 mm in diameter, was grown by a modified Czochralski method in a tri-arc furnace from stoichiometric mixture of the pure elements (99.9% Ho, 99.98% Fe and 99.999% Si). The crystal structure was determined by standard X-ray powder diffraction on a piece of the single crystal crushed into fine powder. The sample was in a single-phase state and had the hexagonal Th2Ni17-type structure. The lattice parameters were found to be as follows: a ¼ 840.2(5) pm, c ¼ 825.2(5) pm, in good agreement with those reported previously for polycrystalline samples [8]. Back-scattered Laue patterns confirming the single-crystalline state of the sample are presented in Fig. 1. These and similar patterns were used to orient the samples along the principal crystallographic directions for magnetization measurements. In order to check chemical composition, the single crystals were studied in secondary and backscattered electron images using a scanning electron microscope (SEM) Superprobe 733 equipped with energy dispersive X-ray spectrometer (EDS) EDAX. Singlephase state of the samples was confirmed. The chemical composition was found to be as 10.3 at.% Ho, 74.0 at.% Fe, 15.7 at.% Si. It agrees well with 2-14-3 stoichiometry, in the case of Si it is 2.98(±0.05). Magnetization along the principal crystallographic axes [100] (a), [120] (b) and [001] (c) was measured by the extraction method in steady magnetic fields up to 9 T at temperatures ranging between 4.2 K and 440 K using a Physical Property Measurement System (Quantum Design PPMS-9). In order to determine the Curie point, temperature dependence of magnetization along the easy axis b was measured up to 600 K by using vibrating sample magnetometer VSM Oven P527 which belongs to PPMS-9 attachments. Magnetization in pulsed magnetic fields up to 58 T (pulse duration 20 ms, initial temperature 4.2 K) was measured at the Dresden High Magnetic Field Laboratory. The high-field magnetometer used for the measurements was described in detail previously [6]. The pulsed-field magnetization was calibrated using the
Fig. 1. X-ray back-scattered Laue patterns along the [100] (a), [120] (b) and [001] (c) axes of the Ho2Fe14Si3 single crystal.
data obtained in steady magnetic fields. The magnetization curves were corrected for demagnetization and presented against the internal field Hi.
A.V. Andreev et al. / Journal of Alloys and Compounds 694 (2017) 761e766
3. Results and discussion Magnetization curves measured along the principal axes at different temperatures are shown in Figs. 2 and 3. One can see that Ho2Fe14Si3 is a highly anisotropic ferrimagnet, the b axis being the easy-magnetization direction, like in Ho2Fe17. The antiparallel arrangement of the Ho and Fe sublattices with predominance of the Fe sublatttice leads to the growth of Ms with temperature because, as temperature increases, MHo drops off faster than MFe. This can be also observed in Fig. 4, which presents temperature dependence of the magnetization of Ho2Fe14Si3 along the principal axes measured in a field of 1 T. The magnetic isotherm taken in a field applied along the b-axis (upper panel of Fig. 2) yields Ms ¼ 8 mB/f.u. at T ¼ 4.2 K. Assuming MHo ¼ 20 mB/f.u. (twice the free-ion moment of Ho3þ), we obtain MFe ¼ Ms þ MHo ¼ 28 mB/f.u., which can be considered as the magnetic moment of the Fe sublattice MFe in Ho2Fe14Si3. This is in agreement with the Ms of R2Fe14Si3 with non-magnetic Y (27 mB/ f.u.) and Lu (26 mB/f.u.) [11] as well as with the Fe sublattice moment in Dy2Fe14Si3, MFe ¼ 28 mB/f.u. [10]. The Curie temperature was determined from the M(T) curve in a low field (Fig. 4) to be TC ¼ 480 K, also in good agreement with the literature [8]. The M(T) el classification of ferrimagdependence (P type according to Ne nets) is typical for R2T17 compound with heavy R (for example, in Er2Fe17 [12]). Figs. 2 and 3 show that the anisotropy within the basal plane vanishes above 160 K, where the magnetization curves along the a and b axes coincide. At low temperatures, the basal-plane magnetization curves of Ho2Fe14Si3 exhibit a characteristic strong
Fig. 2. Magnetization curves of a Ho2Fe14Si3 single crystal measured along the principal axes at T ¼ 4.2e160 K.
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hysteresis with a very low initial susceptibility, an abrupt saturation in a narrow field interval, rectangular hysteresis loops and a drastic exponential decrease of the coercive field with temperature. All these features agree well with the model of high intrinsic coercivity due to narrow domain walls, applicable to highly anisotropic magnets at low temperatures. However, the easy-plane type of magnetic anisotropy is usually not strong enough to produce narrow, several interatomic distances wide domain walls needed for the effective domain-wall pinning in the framework of this model. Accordingly, the coercive field is only 0.25 T at T ¼ 4.2 K with exponential drop to 0.02 T at T ¼ 80 K. The low-field parts of the magnetization curves are very similar to those of Dy2Fe14Si3 described in detail in Ref. [10]. The anisotropy between the basal plane and the c axis persists at much higher temperatures. The M(T) curve along the hard axis [001] displays a maximum at T ¼ 420 K (Fig. 4). It is only above this temperature that the decreasing anisotropy field becomes less than the applied field (1 T), as the compound approaches TC. The main source of the magnetic anisotropy in R-Fe intemetallics is the R sublattice. Nevertheless, the anisotropy contributed by the Fe sublattice is not negligible at elevated temperatures, especially in the case of Ho or Er, which are less anisotropic than Tb, Dy or Tm. The anisotropy of the Fe sublattice can be determined from magnetization curves of a Y2Fe14Si3 single crystal, since yttrium is non-magnetic. These are shown in Fig. 3, for T ¼ 300 K. The
Fig. 3. The same as Fig. 2, for T ¼ 200e350 K. Magnetization curves of Y2Fe14Si3 at 300 K are shown for comparison.
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Fig. 4. Temperature dependence of magnetization of Ho2Fe14Si3 single crystal measured along the principal axes in field of 1 T. The low-field M(T) data along the b axis in the vicinity of TC are shown as well.
anisotropy energy, which equals the area between the easy- and hard-axis curves, amounts to 0.53 MJ m3 and 0.93 MJ m3 for Y2Fe14Si3 and Ho2Fe14Si3, respectively. This means that at room temperature less than 50% of the total anisotropy of Ho2Fe14Si3 comes from the Ho sublattice. High-field magnetization curves of Ho2Fe14Si3 are shown in Fig. 5. The c-axis curve crosses the easy-axis b-curve at 11.5 T. If this value was regarded as anisotropy field, the corresponding uniaxial anisotropy energy (equal to the area of the triangle between the two curves) would amount to 1.0 MJ m3. The c-axis magnetization,
Fig. 5. Magnetization curves of a Ho2Fe14Si3 single crystal measured along the principal axes in pulsed magnetic fields at T ¼ 4.2 K (lines). The symbols represent steadyfield results.
however, continues to grow smoothly above 11.5 T, no phase transition taking place at this point. Such a behavior is characteristic of strongly anisotropic ferrimagnets magnetized in a hard direction [13,14]. In this case the notion of anisotropy field is not meaningful, because the magnetization process involves not only rotation of the total magnetic moment towards the field direction but also field-induced non-collinearity of the ferrimagnetically coupled sublattices. The magnetization along the easy axis b exhibits a first-order phase transition accompanied by a broad hysteresis between 20 and 23 T. A similar but less hysteretic transition is observed at about 29 T when the field is applied along the a axis, the hard magnetization direction in the easy plane. If the general interpretation [6,15] is applied to the b-axis magnetization of Ho2Fe14Si3, it means that the low-field collinear magnetic structure, in which the Ho moments lie along the b axis in the basal plane, anti-aligned with the Fe moments, is broken between 20 and 23 T and a transition takes place to a configuration in which the Ho moments jump to another easy direction and in which Zeeman energy is gained at the expense of intersublattice, Fe-Ho exchange energy. Fig. 6 displays theoretical magnetization curves along the a and b axes up to field-induced ferromagnetic state. The calculations were performed using the standard scheme [6] and consisted in minimizing the following non-equilibrium thermodynamic potential with respect to the sublattice orientation angles a and b:
F ¼ lMFe MHo cosða þ bÞ m0 MFe H cos a m0 MHo H cos b±KHo cos 6 b
(1)
here the first term describes the Fe-Ho exchange, l > 0, while the second and third ones describe Zeeman's interaction with applied magnetic field. The last term is the basal-plane anisotropy energy, KHo > 0, the upper (lower) sign corresponds to the orientation of the applied magnetic field along the a (b) axis, respectively. The model is limited to low temperatures and assumes that jMHoj ¼ MHo ¼ const. ¼ 20 mB/f.u. and jMFej ¼ MFe ¼ const. ¼ 28 mB/ f.u. For the minimization the thermodynamic potential (1) was
Fig. 6. Fits of magnetization curves along the [100] and [120] axes (dashed lines). Solid lines are experimental curves at T ¼ 4.2 K.
A.V. Andreev et al. / Journal of Alloys and Compounds 694 (2017) 761e766
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converted to dimensionless variables,
4 ¼ m cosða þ bÞ h cos a mh cos b±k cos 6 b
(2)
where
f¼
F ; 2 lMFe
h¼
m0 H ; lMFe
m¼
MHo ; MFe
k¼
KHo 2 lMFe
:
(3)
the calculation of the magnetization curves consisted in minimizing the function 4(a,b), Eq. (2), for a given h and substituting the obtained equilibrium orientation angles a and b into an expression for reduced magnetization,
s¼
cos a þ m cos b 1m
(4)
in this model m is a known constant, m ¼ 20/28 ¼ 0.71, while k is an adjustable parameter. To determine k, one should pay attention to the presence of an S-shaped anomaly (at about 47 T) in the magnetization curve along the easy axis b. By comparison with the prediction of the model [6] one concludes that k should not exceed a certain upper limit,
k<
1 2 m 1 m2 ¼ 0:007; 36
(5)
cf. Eq. (A6) of [6]. If this limit was exceeded, the S-shaped anomaly would turn into a discontinuity, which is not observed in our experiment. On the other hand, if k was significantly less than the limit (5), the S-shaped anomaly would be smoothed out, as can be seen in Fig. 5 of [6]. Therefore, k must be slightly less than 0.007. In fact, the best-fit values turned out to be k ¼ 0.005. The best-fit theoretical curves are presented in Fig. 6, along with the corresponding experimental curves. The conversion of the dimensionless s(h) curves to the ‘normal’ physical units was carried out as follows: (i) reduced magnetization s was multiplied by the known spontaneous magnetization at T ¼ 4.2 K, Ms ¼ 8 mB/f.u., to obtain M in mB/f.u.; (ii) reduced magnetic field h was multiplied by the intersublattice molecular field on Ho, lMFe ¼ 63 T, to find m0H in Teslas. This value of the molecular field had been obtained by demanding that the discontinuity in the calculated magnetization curve along the easy axis b, positioned at h ¼ 0.35, coincide with the jump in the corresponding experimental curve, situated at m0H ¼ 22 T. One observes in Fig. 6 a good overall agreement between the theoretical and experimental curves, which corroborates the chosen model. As a further test of its validity, the molecular field on Ho was also determined independently, from temperature dependence of the spontaneous magnetization. First, the temperature dependence of the Fe magnetic moment in Ho2Fe14Si3, MFe(T), was approximated by the spontaneous magnetization Ms(T) of an isostructural compound Y2Fe14Si3, where Y carries no ordered magnetic moment [11]; that Ms(T) was slightly re-normalized to match the Curie temperature and the Fe moment in Ho2Fe14Si3 at T ¼ 4.2 K. The so obtained MFe(T) in Ho2Fe14Si3 is shown in Fig. 7. Then the moment of the Ho sublattice was found by subtracting Ms(T) of Ho2Fe14Si3 from the previously obtained MFe(T). The resulting MHo(T) curve is also shown in Fig. 7. This curve was fitted to the following expression
MHo ðTÞ ¼ 20mB B8
10mB lMFe ðTÞ ; kT
(6)
where B8(x) is the Brilluoin function for J ¼ 8, as appropriate for Ho3þ. The best fit of the experimental data, shown in Fig. 7,
Fig. 7. Temperature dependence of the spontaneous magnetic moment Ms of Ho2Fe14Si3 and of the moments of the Fe and Ho sublattices.
corresponds to lMFe(0) ¼ 61 ± 2 T. The two values of the molecular field are close to each other, which confirms that our model is a reasonable one. A yet another fact supporting the model is that the intersublattice molecular field constant is the same in Ho2Fe14Si3 and in the parent compound Ho2Fe17 [6]: l ¼ 2.2 T f.u./mB. As against that, the basal-plane anisotropy constants KHo turn out to be very different for the two compounds. Thus, for Ho2Fe14Si3 2 Þ z 6 K/f.u., whereas the same quantity for we find KHo ¼ k ðlMFe Ho2Fe17 was found to be at least an order of magnitude higher, KHo >~40 K/f.u. [6]. Both values refer to T ¼ 4.2 K, which theoretically is equivalent to T ¼ 0. In that case KHo is directly proportional to the crystal field parameter A66 [16], or rather, to its mean value for the two non-equivalent Ho sites, 2b and 2d. By Eq. (1) of [6],
A66 ¼
A66 ðbÞ þ A66 ðdÞ K ¼ 4:29 Ho 2 r6
(7)
with hr 6 i ¼ 5:379a60 [17]. Hence we find for Ho2Fe14Si3 A66 ¼ 5 6 6 Ka6 0 , while for Ho2Fe17 A6 < ~30 Ka0 . Our results thus demonstrate that crystal field is extremely sensitive to isostructural substitutions. An earlier example of such sensitivity was concerned with second-order crystal field [18] but now the effect appears to be quite general. 4. Conclusions The dilution of the iron sublattice in Ho2Fe17 with Si shifts the field-induced first-order phase transitions towards lower fields. The Fe sublattice magnetization is reduced roughly in proportion to the content of Fe; the intersublattice coupling constant l is unchanged to within the error bar. For all that, the basal-plane anisotropy constant KHo is reduced drastically, by at least one order of magnitude. As a result, the magnetization curves of Ho2Fe14Si3 are qualitatively different to those of the parent compound. In Ho2Fe17 the basal-plane curves have a pronounced strongly anisotropic character, with the highest possible number of discontinuities: 3 in the easy direction [120] and 2 in the hard one [100]. On the contrary, Ho2Fe14Si3 has typical weakly anisotropic
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magnetization curves, with a single discontinuity in both directions. Acknowledgements The steady-field measurements were partly performed in MLTL (http://mltl.eu/), which is supported within the program of Czech Research Infrastructures (Project No. LM2011025). The work was supported by Czech Science Foundation (grants P16-03593S) and by the High Magnetic Field Laboratory Dresden (HLD) at HZDR, member of the European Magnetic Field Laboratory (EMFL). References [1] M.D. Kuz'min, Phys. Rev. B 51 (1995) 8904. [2] K. Clausen, O.V. Nielsen, J. Magn. Magn. Mater. 23 (1981) 237. [3] S. Sinnema, Magnetic Interactions in R2T17 and R2T14B Intermetallic Compounds, PhD thesis, University of Amsterdam, 1988. [4] S. Sinnema, J.J.M. Franse, R.J. Radwanski, A. Menovsky, F.R. de Boer, J. Phys. F Metal Phys. 17 (1987) 233.
d, O. Mikulina, Z. Arnold, B. García-Landa, M.R. Ibarra, J. Appl. Phys. [5] J. Kamara 85 (1999) 4874. [6] Y. Skourski, M.D. Kuz'min, K.P. Skokov, A.V. Andreev, J. Wosnitza, Phys. Rev. B 83 (2011) 214420. [7] T.H. Jacobs, K.H.J. Buschow, G.F. Zhou, X. Li, F.R. de Boer, J. Magn. Magn. Mater. 116 (1992) 220. [8] B.G. Shen, B. Liang, Z.H. Cheng, T.Y. Gong, H. Tang, F.R. De Boer, K.H.J. Buschow, Solid State Commun. 103 (1997) 71. [9] J.M.M. Franse, F.R. de Boer, P.H. Frings, R. Gersdorf, A. Menovsky, F.A. Muller, R.J. Radwanski, S. Sinnema, Phys. Rev. B 31 (1985) 4347. [10] A.V. Andreev, M.D. Kuz'min, S. Yoshii, E.A. Tereshina, K. Kindo, M. Hagiwara, F.R. de Boer, J. Alloys Comp. 509 (2011) 5042. [11] A.V. Andreev, J. Alloys Comp. 475 (2009) 13. [12] P. Alvarez-Alonso, P. Gorria, J.A. Blanco, J. Sanchez-Marcos, G.J. Cuello, I. Puente-Orench, J.A. Rodriguez-Velamazan, G. Garbarino, I. de Pedro, J. Rodriguez Fernandez, J.L. Sanchez Llamazares, Phys. Rev. B 86 (2012) 184411. [13] M.D. Kuz'min, J. Magn. Magn. Mater. 323 (2011) 1068. [14] M.D. Kuz’min, J. Appl. Phys. 111 (2012) 043904. [15] M.D. Kuz’min, Y. Skourski, K.P. Skokov, K.-H. Müller, Phys. Rev. B 75 (2007) 184439. [16] M.S.S. Brooks, J. Phys. C 2 (1969) 1016. [17] A.J. Freeman, J.P. Desclaux, J. Magn. Magn. Mater. 12 (1979) 11. [18] M.D. Kuz’min, M. Richter, K.H.J. Buschow, Solid State Commun. 113 (1999) 47.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Magnetic properties of a Ho2Fe14Si3 single crystal A.V. Andreev a, *, D.I. Gorbunov b, Y. Skourski b, M.D. Kuz'min c, E.A. Tereshina a, M.S. Henriques a a
Institute of Physics, Academy of Sciences, Na Slovance 2, 182 21 Prague, Czechia Dresden High Magnetic Field Laboratory (HLD-EMFL), Helmholtz-Zentrum, Dresden-Rossendorf, D-01314 Dresden, Germany c Aix-Marseille Universit e, IM2NP, UMR CNRS 7334, 13397 Marseille, France b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 June 2016 Received in revised form 6 October 2016 Accepted 8 October 2016 Available online 10 October 2016
Magnetization of a Ho2Fe14Si3 single crystal was measured in a steady magnetic field of up to 9 T and in pulsed fields of up to 60 T applied along the principal axes. Ho2Fe14Si3 is a ferrimagnet below TC ¼ 480 K, has a spontaneous magnetic moment of about 8 mB/f.u. (at T ¼ 4.2 K) and exhibits a large easy-plane magnetic anisotropy. There is also a certain anisotropy within the basal plane, the b axis [120] being the easy-magnetization direction. In fields applied along the a and b axes field-induced first-order phase transitions are observed at 29 T and at 22 T, respectively. Along the easy axis b we observe also an Sshaped anomaly at about 47 T, which does not correspond to a phase transition. A simple model predicts that the two observed first-order transitions are the only ones taking place in Ho2Fe14Si3; the magnetization should subsequently grow continuously and arrive at saturation at ~100 T. This is in stark contrast to the behavior of the parent compound Ho2Fe17, where as many as three sequential first-order transitions are expected for Hjjb. The reason for the disparity is that the basal-plane anisotropy constant KHo is at least one order of magnitude smaller in Ho2Fe14Si3 than it is in Ho2Fe17. © 2016 Elsevier B.V. All rights reserved.
Keywords: Rare-earth intermetallics R2T17 High magnetic fields Field-induced transitions Magnetic anisotropy
1. Introduction The magnetism of rare earth (R) intermetallic compounds with iron and/or cobalt is of interest from two points of view. Firstly, because of the high application potential of these materials, e.g., as permanent magnets (primarily R2Fe14B-based). Secondly, from a purely academic prospective, these are systems containing two entirely distinct kinds of electrons: (i) the 4f electrons, localized within the R atoms, and (ii) the itinerant 3d electrons of Fe or Co. The competition of intra- and inter-sublattice exchange interactions with each other and with the crystal field often brings about spontaneous and/or field-induced magnetic phase transitions. Research into these phenomena is conducive to deeper understanding of the fundamental aspects of magnetism but it is also of great practical importance. Suffice it to recall that the anisotropy (and coercivity) of permanent magnets at and above room temperature is proportional to the leading crystal field parameter A20 times the square of the inter-sublattice exchange field [1]. Ho2Fe17 crystallizes in the hexagonal crystal structure of the
* Corresponding author. E-mail address: [email protected] (A.V. Andreev). http://dx.doi.org/10.1016/j.jallcom.2016.10.069 0925-8388/© 2016 Elsevier B.V. All rights reserved.
Th2Ni17 type, characteristic of the heavy R. Magnetic measurements on single crystals showed that in the ground state the spontaneous magnetic moment, Ms ¼ 16.0e18.5 mB/f.u. (per formula unit), lies in the basal plane along the [210] direction (or the b axis in the orthorhombic coordinates) [2e6]. The compound is a collinear ferrimagnet below the Curie temperature, TC ¼ 325e335 K [2,5,7,8]. The total magnetic moment is parallel to that of the Fe sublattice. Taking Ms ¼ 18 mB/f.u. ([6]) and the magnetic moment of the Ho sublattice MHo ¼ 20 mB/f.u. (as 2 free-ion moments of Ho3þ), the Fe sublattice moment MFe is found to be 38 mB/f.u. In such compounds, field-induced phase transitions are expected, from the collinear ferrimagnetic structure, through intermediate canted structures, to the final collinear ferromagnetic configuration. This was observed in Ho2Co17 [9] and in several other ferrimagnetic R2Fe17 and R2Co17 compounds with the easy-plane type of anisotropy. The high-field magnetic transitions that take place in these compounds in a magnetic field applied within the basal-plane are the result of competition between the Zeeman energy (strength of the applied field) and the energy of the 3d-4f exchange interaction. In particular, step-wise anomalies were observed in the high-field magnetization curves of Ho2Fe17: at 45 T when the field was applied along the b axis, and at 55 T when it was along the a axis [6]. In the maximum available field (60 T) the magnetization reached 34 mB/
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f.u.; this is still far below the value characteristic of the collinear ferromagnetic state, 48 mB. Magnetization of the Si solid solutions in R2Fe17, R2Fe14Si3, was studied on polycrystalline samples [8]. A strong modification of both the intra- and inter-sublattice interactions was found in R2Fe14Si3 as compared with R2Fe17. The effect is rather complicated, because the Fe sublattice moment is weakened by the dilution with the non-magnetic Si, whereas the Fe-Fe exchange interaction is unexpectedly enhanced e so the Curie temperature rises from 330 K in Ho2Fe17 to 477 K in Ho2Fe14Si3 [8]. If it is true that the strength of the inter-sublattice exchange coupling is reduced by the dilution of the Fe sublattice, then in the silicides the transitions should take place in lower, more easily attainable fields. Previously we studied the high-field magnetization of Dy2Fe14Si3 [10] and found that the transition fields had decreased in comparison with those in the binary compound Dy2Fe17. Thus, the critical field along the a axis amounted to 33 T and 54 T, respectively, in Dy2Fe14Si3 and in Dy2Fe17. Along the b axis, the transition was observed at 39 T in Dy2Fe14Si3, whereas in Dy2Fe17 it did not take place up to 60 T. If a similar behavior is valid for the Ho compounds, we can expect to see more transitions in a field up to 60 T, get closer to the forced ferromagnetic state and check in this way our description of the high-field magnetization process in R2Fe17 developed in Refs. [6,10]. In the present work we measured the magnetization of Ho2Fe14Si3 in steady and pulsed magnetic fields applied along the principal crystallographic axes. 2. Experimental A single crystal of Ho2Fe14Si3, 25 mm long and 4 mm in diameter, was grown by a modified Czochralski method in a tri-arc furnace from stoichiometric mixture of the pure elements (99.9% Ho, 99.98% Fe and 99.999% Si). The crystal structure was determined by standard X-ray powder diffraction on a piece of the single crystal crushed into fine powder. The sample was in a single-phase state and had the hexagonal Th2Ni17-type structure. The lattice parameters were found to be as follows: a ¼ 840.2(5) pm, c ¼ 825.2(5) pm, in good agreement with those reported previously for polycrystalline samples [8]. Back-scattered Laue patterns confirming the single-crystalline state of the sample are presented in Fig. 1. These and similar patterns were used to orient the samples along the principal crystallographic directions for magnetization measurements. In order to check chemical composition, the single crystals were studied in secondary and backscattered electron images using a scanning electron microscope (SEM) Superprobe 733 equipped with energy dispersive X-ray spectrometer (EDS) EDAX. Singlephase state of the samples was confirmed. The chemical composition was found to be as 10.3 at.% Ho, 74.0 at.% Fe, 15.7 at.% Si. It agrees well with 2-14-3 stoichiometry, in the case of Si it is 2.98(±0.05). Magnetization along the principal crystallographic axes [100] (a), [120] (b) and [001] (c) was measured by the extraction method in steady magnetic fields up to 9 T at temperatures ranging between 4.2 K and 440 K using a Physical Property Measurement System (Quantum Design PPMS-9). In order to determine the Curie point, temperature dependence of magnetization along the easy axis b was measured up to 600 K by using vibrating sample magnetometer VSM Oven P527 which belongs to PPMS-9 attachments. Magnetization in pulsed magnetic fields up to 58 T (pulse duration 20 ms, initial temperature 4.2 K) was measured at the Dresden High Magnetic Field Laboratory. The high-field magnetometer used for the measurements was described in detail previously [6]. The pulsed-field magnetization was calibrated using the
Fig. 1. X-ray back-scattered Laue patterns along the [100] (a), [120] (b) and [001] (c) axes of the Ho2Fe14Si3 single crystal.
data obtained in steady magnetic fields. The magnetization curves were corrected for demagnetization and presented against the internal field Hi.
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3. Results and discussion Magnetization curves measured along the principal axes at different temperatures are shown in Figs. 2 and 3. One can see that Ho2Fe14Si3 is a highly anisotropic ferrimagnet, the b axis being the easy-magnetization direction, like in Ho2Fe17. The antiparallel arrangement of the Ho and Fe sublattices with predominance of the Fe sublatttice leads to the growth of Ms with temperature because, as temperature increases, MHo drops off faster than MFe. This can be also observed in Fig. 4, which presents temperature dependence of the magnetization of Ho2Fe14Si3 along the principal axes measured in a field of 1 T. The magnetic isotherm taken in a field applied along the b-axis (upper panel of Fig. 2) yields Ms ¼ 8 mB/f.u. at T ¼ 4.2 K. Assuming MHo ¼ 20 mB/f.u. (twice the free-ion moment of Ho3þ), we obtain MFe ¼ Ms þ MHo ¼ 28 mB/f.u., which can be considered as the magnetic moment of the Fe sublattice MFe in Ho2Fe14Si3. This is in agreement with the Ms of R2Fe14Si3 with non-magnetic Y (27 mB/ f.u.) and Lu (26 mB/f.u.) [11] as well as with the Fe sublattice moment in Dy2Fe14Si3, MFe ¼ 28 mB/f.u. [10]. The Curie temperature was determined from the M(T) curve in a low field (Fig. 4) to be TC ¼ 480 K, also in good agreement with the literature [8]. The M(T) el classification of ferrimagdependence (P type according to Ne nets) is typical for R2T17 compound with heavy R (for example, in Er2Fe17 [12]). Figs. 2 and 3 show that the anisotropy within the basal plane vanishes above 160 K, where the magnetization curves along the a and b axes coincide. At low temperatures, the basal-plane magnetization curves of Ho2Fe14Si3 exhibit a characteristic strong
Fig. 2. Magnetization curves of a Ho2Fe14Si3 single crystal measured along the principal axes at T ¼ 4.2e160 K.
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hysteresis with a very low initial susceptibility, an abrupt saturation in a narrow field interval, rectangular hysteresis loops and a drastic exponential decrease of the coercive field with temperature. All these features agree well with the model of high intrinsic coercivity due to narrow domain walls, applicable to highly anisotropic magnets at low temperatures. However, the easy-plane type of magnetic anisotropy is usually not strong enough to produce narrow, several interatomic distances wide domain walls needed for the effective domain-wall pinning in the framework of this model. Accordingly, the coercive field is only 0.25 T at T ¼ 4.2 K with exponential drop to 0.02 T at T ¼ 80 K. The low-field parts of the magnetization curves are very similar to those of Dy2Fe14Si3 described in detail in Ref. [10]. The anisotropy between the basal plane and the c axis persists at much higher temperatures. The M(T) curve along the hard axis [001] displays a maximum at T ¼ 420 K (Fig. 4). It is only above this temperature that the decreasing anisotropy field becomes less than the applied field (1 T), as the compound approaches TC. The main source of the magnetic anisotropy in R-Fe intemetallics is the R sublattice. Nevertheless, the anisotropy contributed by the Fe sublattice is not negligible at elevated temperatures, especially in the case of Ho or Er, which are less anisotropic than Tb, Dy or Tm. The anisotropy of the Fe sublattice can be determined from magnetization curves of a Y2Fe14Si3 single crystal, since yttrium is non-magnetic. These are shown in Fig. 3, for T ¼ 300 K. The
Fig. 3. The same as Fig. 2, for T ¼ 200e350 K. Magnetization curves of Y2Fe14Si3 at 300 K are shown for comparison.
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Fig. 4. Temperature dependence of magnetization of Ho2Fe14Si3 single crystal measured along the principal axes in field of 1 T. The low-field M(T) data along the b axis in the vicinity of TC are shown as well.
anisotropy energy, which equals the area between the easy- and hard-axis curves, amounts to 0.53 MJ m3 and 0.93 MJ m3 for Y2Fe14Si3 and Ho2Fe14Si3, respectively. This means that at room temperature less than 50% of the total anisotropy of Ho2Fe14Si3 comes from the Ho sublattice. High-field magnetization curves of Ho2Fe14Si3 are shown in Fig. 5. The c-axis curve crosses the easy-axis b-curve at 11.5 T. If this value was regarded as anisotropy field, the corresponding uniaxial anisotropy energy (equal to the area of the triangle between the two curves) would amount to 1.0 MJ m3. The c-axis magnetization,
Fig. 5. Magnetization curves of a Ho2Fe14Si3 single crystal measured along the principal axes in pulsed magnetic fields at T ¼ 4.2 K (lines). The symbols represent steadyfield results.
however, continues to grow smoothly above 11.5 T, no phase transition taking place at this point. Such a behavior is characteristic of strongly anisotropic ferrimagnets magnetized in a hard direction [13,14]. In this case the notion of anisotropy field is not meaningful, because the magnetization process involves not only rotation of the total magnetic moment towards the field direction but also field-induced non-collinearity of the ferrimagnetically coupled sublattices. The magnetization along the easy axis b exhibits a first-order phase transition accompanied by a broad hysteresis between 20 and 23 T. A similar but less hysteretic transition is observed at about 29 T when the field is applied along the a axis, the hard magnetization direction in the easy plane. If the general interpretation [6,15] is applied to the b-axis magnetization of Ho2Fe14Si3, it means that the low-field collinear magnetic structure, in which the Ho moments lie along the b axis in the basal plane, anti-aligned with the Fe moments, is broken between 20 and 23 T and a transition takes place to a configuration in which the Ho moments jump to another easy direction and in which Zeeman energy is gained at the expense of intersublattice, Fe-Ho exchange energy. Fig. 6 displays theoretical magnetization curves along the a and b axes up to field-induced ferromagnetic state. The calculations were performed using the standard scheme [6] and consisted in minimizing the following non-equilibrium thermodynamic potential with respect to the sublattice orientation angles a and b:
F ¼ lMFe MHo cosða þ bÞ m0 MFe H cos a m0 MHo H cos b±KHo cos 6 b
(1)
here the first term describes the Fe-Ho exchange, l > 0, while the second and third ones describe Zeeman's interaction with applied magnetic field. The last term is the basal-plane anisotropy energy, KHo > 0, the upper (lower) sign corresponds to the orientation of the applied magnetic field along the a (b) axis, respectively. The model is limited to low temperatures and assumes that jMHoj ¼ MHo ¼ const. ¼ 20 mB/f.u. and jMFej ¼ MFe ¼ const. ¼ 28 mB/ f.u. For the minimization the thermodynamic potential (1) was
Fig. 6. Fits of magnetization curves along the [100] and [120] axes (dashed lines). Solid lines are experimental curves at T ¼ 4.2 K.
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converted to dimensionless variables,
4 ¼ m cosða þ bÞ h cos a mh cos b±k cos 6 b
(2)
where
f¼
F ; 2 lMFe
h¼
m0 H ; lMFe
m¼
MHo ; MFe
k¼
KHo 2 lMFe
:
(3)
the calculation of the magnetization curves consisted in minimizing the function 4(a,b), Eq. (2), for a given h and substituting the obtained equilibrium orientation angles a and b into an expression for reduced magnetization,
s¼
cos a þ m cos b 1m
(4)
in this model m is a known constant, m ¼ 20/28 ¼ 0.71, while k is an adjustable parameter. To determine k, one should pay attention to the presence of an S-shaped anomaly (at about 47 T) in the magnetization curve along the easy axis b. By comparison with the prediction of the model [6] one concludes that k should not exceed a certain upper limit,
k<
1 2 m 1 m2 ¼ 0:007; 36
(5)
cf. Eq. (A6) of [6]. If this limit was exceeded, the S-shaped anomaly would turn into a discontinuity, which is not observed in our experiment. On the other hand, if k was significantly less than the limit (5), the S-shaped anomaly would be smoothed out, as can be seen in Fig. 5 of [6]. Therefore, k must be slightly less than 0.007. In fact, the best-fit values turned out to be k ¼ 0.005. The best-fit theoretical curves are presented in Fig. 6, along with the corresponding experimental curves. The conversion of the dimensionless s(h) curves to the ‘normal’ physical units was carried out as follows: (i) reduced magnetization s was multiplied by the known spontaneous magnetization at T ¼ 4.2 K, Ms ¼ 8 mB/f.u., to obtain M in mB/f.u.; (ii) reduced magnetic field h was multiplied by the intersublattice molecular field on Ho, lMFe ¼ 63 T, to find m0H in Teslas. This value of the molecular field had been obtained by demanding that the discontinuity in the calculated magnetization curve along the easy axis b, positioned at h ¼ 0.35, coincide with the jump in the corresponding experimental curve, situated at m0H ¼ 22 T. One observes in Fig. 6 a good overall agreement between the theoretical and experimental curves, which corroborates the chosen model. As a further test of its validity, the molecular field on Ho was also determined independently, from temperature dependence of the spontaneous magnetization. First, the temperature dependence of the Fe magnetic moment in Ho2Fe14Si3, MFe(T), was approximated by the spontaneous magnetization Ms(T) of an isostructural compound Y2Fe14Si3, where Y carries no ordered magnetic moment [11]; that Ms(T) was slightly re-normalized to match the Curie temperature and the Fe moment in Ho2Fe14Si3 at T ¼ 4.2 K. The so obtained MFe(T) in Ho2Fe14Si3 is shown in Fig. 7. Then the moment of the Ho sublattice was found by subtracting Ms(T) of Ho2Fe14Si3 from the previously obtained MFe(T). The resulting MHo(T) curve is also shown in Fig. 7. This curve was fitted to the following expression
MHo ðTÞ ¼ 20mB B8
10mB lMFe ðTÞ ; kT
(6)
where B8(x) is the Brilluoin function for J ¼ 8, as appropriate for Ho3þ. The best fit of the experimental data, shown in Fig. 7,
Fig. 7. Temperature dependence of the spontaneous magnetic moment Ms of Ho2Fe14Si3 and of the moments of the Fe and Ho sublattices.
corresponds to lMFe(0) ¼ 61 ± 2 T. The two values of the molecular field are close to each other, which confirms that our model is a reasonable one. A yet another fact supporting the model is that the intersublattice molecular field constant is the same in Ho2Fe14Si3 and in the parent compound Ho2Fe17 [6]: l ¼ 2.2 T f.u./mB. As against that, the basal-plane anisotropy constants KHo turn out to be very different for the two compounds. Thus, for Ho2Fe14Si3 2 Þ z 6 K/f.u., whereas the same quantity for we find KHo ¼ k ðlMFe Ho2Fe17 was found to be at least an order of magnitude higher, KHo >~40 K/f.u. [6]. Both values refer to T ¼ 4.2 K, which theoretically is equivalent to T ¼ 0. In that case KHo is directly proportional to the crystal field parameter A66 [16], or rather, to its mean value for the two non-equivalent Ho sites, 2b and 2d. By Eq. (1) of [6],
A66 ¼
A66 ðbÞ þ A66 ðdÞ K ¼ 4:29 Ho 2 r6
(7)
with hr 6 i ¼ 5:379a60 [17]. Hence we find for Ho2Fe14Si3 A66 ¼ 5 6 6 Ka6 0 , while for Ho2Fe17 A6 < ~30 Ka0 . Our results thus demonstrate that crystal field is extremely sensitive to isostructural substitutions. An earlier example of such sensitivity was concerned with second-order crystal field [18] but now the effect appears to be quite general. 4. Conclusions The dilution of the iron sublattice in Ho2Fe17 with Si shifts the field-induced first-order phase transitions towards lower fields. The Fe sublattice magnetization is reduced roughly in proportion to the content of Fe; the intersublattice coupling constant l is unchanged to within the error bar. For all that, the basal-plane anisotropy constant KHo is reduced drastically, by at least one order of magnitude. As a result, the magnetization curves of Ho2Fe14Si3 are qualitatively different to those of the parent compound. In Ho2Fe17 the basal-plane curves have a pronounced strongly anisotropic character, with the highest possible number of discontinuities: 3 in the easy direction [120] and 2 in the hard one [100]. On the contrary, Ho2Fe14Si3 has typical weakly anisotropic
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magnetization curves, with a single discontinuity in both directions. Acknowledgements The steady-field measurements were partly performed in MLTL (http://mltl.eu/), which is supported within the program of Czech Research Infrastructures (Project No. LM2011025). The work was supported by Czech Science Foundation (grants P16-03593S) and by the High Magnetic Field Laboratory Dresden (HLD) at HZDR, member of the European Magnetic Field Laboratory (EMFL). References [1] M.D. Kuz'min, Phys. Rev. B 51 (1995) 8904. [2] K. Clausen, O.V. Nielsen, J. Magn. Magn. Mater. 23 (1981) 237. [3] S. Sinnema, Magnetic Interactions in R2T17 and R2T14B Intermetallic Compounds, PhD thesis, University of Amsterdam, 1988. [4] S. Sinnema, J.J.M. Franse, R.J. Radwanski, A. Menovsky, F.R. de Boer, J. Phys. F Metal Phys. 17 (1987) 233.
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